BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Raimundo Briceño (Pontificia Universidad Católica de Chile) DTSTART:20210128T190000Z DTEND:20210128T200000Z DTSTAMP:20260423T035756Z UID:OLS/40 DESCRIPTION:Title: Dis mantlability\, connectedness\, and mixing in relational structures\nby Raimundo Briceño (Pontificia Universidad Católica de Chile) as part of Online logic seminar\n\n\nAbstract\nThe Constraint Satisfaction Problem (C SP) and its counting counterpart appears under different guises in many ar eas of mathematics\, computer science\, and elsewhere. Its structural and algorithmic properties have demonstrated to play a crucial role in many of those applications. For instance\, in the decision CSPs\, structural prop erties of the relational structures involved —like\, for example\, disma ntlability— and their logical characterizations have been instrumental f or determining the complexity and other properties of the problem. Topolog ical properties of the solution set such as connectedness are related to t he hardness of CSPs over random structures. Additionally\, in approximate counting and statistical physics\, where CSPs emerge in the form of spin s ystems\, mixing properties and the uniqueness of Gibbs measures have been heavily exploited for approximating partition functions and free energy.\n \nIn spite of the great diversity of those features\, there are some eerie similarities between them. These were observed and made more precise in t he case of graph homomorphisms by Brightwell and Winkler\, who showed that dismantlability of the target graph\, connectedness of the set of homomor phisms\, and good mixing properties of the corresponding spin system are a ll equivalent. In this talk we go a step further and demonstrate similar c onnections for arbitrary CSPs. This requires a much deeper understanding o f dismantling and the structure of the solution space in the case of relat ional structures\, and also new refined concepts of mixing. In addition\, we develop properties related to the study of valid extensions of a given partially defined homomorphism\, an approach that turns out to be novel ev en in the graph case. We also add to the mix the combinatorial property of finite duality and its logic counterpart\, FO-definability\, studied by L arose\, Loten\, and Tardif. This is joint work with Andrei Bulatov\, Víct or Dalmau\, and Benoît Larose.\n LOCATION:https://researchseminars.org/talk/OLS/40/ END:VEVENT END:VCALENDAR